Turkish Journal of Mathematics
Abstract
Let $J_\nu(z)$ denote the Bessel function of the first kind of order $\nu.$ In this paper, our aim is to determine the radii of starlikeness and convexity for three kind of normalization of the function $N_\nu(z)=az^{2}J_{\nu }^{\prime \prime }(z)+bzJ_{\nu }^{\prime }(z)+cJ_{\nu }(z)$ in the case where zeros are all real except for a single pair, which are conjugate purely imaginary. The key tools in the proof of our main results are the Mittag-Leffler expansion for function $N_\nu(z)$ and properties of real and complex zeros of it.
DOI
10.55730/1300-0098.3130
Keywords
Normalized Bessel functions of the fist kind, convex functions, starlike functions, zeros of Bessel function derivatives, radius
First Page
894
Last Page
911
Recommended Citation
KAZIMOĞLU, S, & DENİZ, E (2022). The radii of starlikeness and convexity of the functions including derivatives of Bessel functions. Turkish Journal of Mathematics 46 (3): 894-911. https://doi.org/10.55730/1300-0098.3130
